Padding: Update input area on empty screen and in progress chat

<img width="1053" height="356" alt="Image" src="https://github.com/user-attachments/assets/bc82c28b-a7d9-4940-8b00-98ea4ba0aa33" />
<img width="912" height="201" alt="Image" src="https://github.com/user-attachments/assets/4fe84d26-3125-467d-bbce-c83bd824fb96" />

Figma: https://www.figma.com/design/lWE17f1tRRDXWsbxTcbsmo/Polish-Push-May-2026?node-id=400-208